# Rattiners review for the certification examination - Rattiner J.

ISBN 0-471-27265-5

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(a) FV = $1,000, PMT = $100, N = 5, I = 12 ^ solve for PV

(b) The price of the bond is $927.90. The bond is said to be selling at a discount (lower price than face value). In this situation, an investor will be competitive with similar bonds and yield 12 percent on the investment.

(3) Bonds generally pay interest twice a year (semiannually) instead of once a year. The equation previously presented is modified slightly by adjusting the total number of periods and the amount of each payment. The total number of periods becomes 10 (2 x 5 years), the amount of payment is $50 ($100 coupon 2), and the yield becomes 6 percent (12% + 2). The calculation is as follows: FV = $1,000, PMT = $50, N = 10,

I = 6 ^ solve for PV = - $926.39.

2. Dividend growth models

A. Valuing stock with no dividend growth

(1) This model uses the same equation as that used to value a preferred stock. The only difference is the required rate of return on the common stock, which tends to account for more risk than that of a preferred stock.

150 - Investment Planning

(2) V = D k

B. Stock value, assuming a one-year holding period

(1) The value of a stock is the present value of any dividend received during the year, plus the present value of the price of stock at the end of the year. The valuation equation is

Dividend to be received Year-end sale price

V =------------------------------1-------------------------------------

(1 + ke) 1 11 + ke)1

(2) Example: What is the value of a stock that last year paid a $1 dividend that is expected to grow 10 percent next year? The stock will be selling at $25 at year end. The risk-free rate of interest is 4 percent, the market return is 10 percent, and the stock’s beta is 1.2.

(a) Step 1. Solve for the discount rate. Kstock = 4% + (10% - 4%)1.1 = 10.6%.

(b) Step 2. Add the future dividend to future stock price. D1 = $1(1.1) = $1.10, so add future value of stock and dividend to get $26.10 ($1.10 + $25).

$26.10

(c) Step 3. Find the present value. + q þá) 1 = $23.59.

C. Valuing stock with constant dividend growth

(1) The constant growth dividend discount model assumes that dividends may increase at a fixed rate on an annual basis in the future. Example: If the latest dividend is $1 and dividends grow at an annual rate of 5 percent, the dividend next year is

(a) $1(1 + 0.05)1 = $1.05

(b) The dividend in the second year is $1(1 + 0.05)2 = $1.10.

(c) The pattern of 5 percent growth is expected to continue into the future.

(2) The value of a common stock with a constant rate of growth can be determined by

òã D0 (1 +g) D1

V =--------------or -

k - g k - g

where D0 is the latest dividend paid per share, D1 is the expected dividend per share for year 1, k is the required rate of return on the stock, and g is the expected growth rate of dividends.

(3) Example: What is the value of a stock that paid a $2 dividend last year, which is

expected to grow annually at 5 percent? The risk-free rate is 4 percent and the expected return on the market is 10 percent. The stock’s beta is 1.7.

(a) Step 1. Determine k by using CAPM.

kstock Rrisk free + betastock (Rmarket Rrisk free)

kstock = 4% + 1.7(10% - 4%) = 14.2%

(b) Step 2. Use the constant dividend discount model.

$2 (1 + 0.05)

V0 = —--------------- = $22.82

0 0.142 - 0.05

(c) If the stock is bought at a lower price than $22.82, its expected return will exceed 14.2 percent. If the stock is bought at a higher price than $22.82, its expected return will not exceed 14.2 percent. For example, if the stock price is currently $25, the

$2

expected return is (E(r)) = -— + 0.05 = 13% .

$25

Topic 45: Bond and Stock Valuation Methods - 151

(4) The constant growth dividend discount model (DDM) has the following assumptions:

(a) The stock pays dividends, and they grow constantly forever.

(b) The constant growth rate continues for an infinite period.

(c) k must be greater than g.

D. Temporary supernormal growth

(1) Some companies have supergrowth in the early years that levels out in later years. For these companies, k is less than g. Therefore, the constant growth DDM does not work.

D(n + 1)

V1 = D1 , D2 + + (k — g2

growth (l + k) + (l + k) 2 + + (1 + ke)n

(2) Example: For years 1 through 4, g = 25 percent; for years 5 on, g = 5 percent; D1 = $1,

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